Find the slope of the curve x^2 + xy + y^2 = 7 at (1,2)
x^2 + xy + y^2 = 7
The slope is the derivative at (1,2).
Let us diffirentiate with respect to x:
=(x^2 + xy + y^2)' =...
(The entire section contains 60 words.)
check Approved by eNotes Editorial
To do this problem we first apply the product rule:
d ( xy) / dx = y + x*dy/dx
to find the derivative of x^2 + xy + y^2 = 7.
So the derivative of x^2 + xy + y^2 = 7 is
2x + x*dy/dx +y + 2y* dy/dx =0
Now taking dy/dx to one side,
=> dy/dx( x +2y ) = -x^2 -xy - y^2
=> dy/dx = (-x^2 -xy - y^2) / (x+2y)
dy/dx = (-x^2 -xy - y^2) / (x+2y)
=>( - 1^2 - 1*2 - 2^2)/ (1+ 4)
=> (-2 -2 -4 )/5
Therefore the required slope is -8/5